Chapter 24.3, Problem 26SSC

Interpretation Introduction

Interpretation:

The energy change associated with a change in mass of $1.00\text{mg}$ needs to be explained.

Concept introduction:

Albert Einstein’s equation relates mass and energy. According to this equation any reaction produces or consumes energy due to a loss or gain in mass. Energy and mass are equivalent. The equation is as follows:

$\Delta E=\Delta m{c}^2$

Here, $\Delta E$ and $\Delta m$ represents change in energy and change in mass respectively, c represents the speed of light.

Answer to Problem 26SSC

Energy change associated with a change in mass of $1.00\text{mg}$ is $9\times {10}^8\text{J}$.

Explanation of Solution

Albert Einstein’s equation is as follows:

$\Delta E=\Delta m{c}^2$.......(1)

Given,

$\begin{array}{l}\Delta m=1.00\text{mg}\\ {\text{=10}}^{-6}\text{kg}\\ c=3\times {10}^8\text{m/s}\\ \Delta E=?\end{array}$

Substitute the above values in equation (1).

$\begin{array}{c}\Delta E=\Delta m{c}^2\\ ={10}^{-6}\text{kg}{\left(3\times {10}^8\text{m/s}\right)}^2\\ =9\times {10}^{16-8}\text{kg}\text{.}{\text{m}}^{\text{2}}{\text{/s}}^{\text{2}}\\ =9\times {10}^8\text{J}\end{array}$

Therefore, $\Delta E$ value is $9\times {10}^8\text{J}$.

Conclusion

Energy change associated with a change in mass of $1.00\text{mg}$ is $9\times {10}^8\text{J}$.